An eight-component relativistic wave equation for spin-1/2 particles II

Journal of Physics A: Mathematical and General

Volumn 29, Issue 1, 1996, Pages 169-192

  Staudte, D S ^a,b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21844489784     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/29/1/018     Document Type: Article

References (22)

1. Robson B A and Staudte D S 1996 J. Phys. A: Math. Gen. 29 157
2. Dirac P A M 1928 Proc. R. Soc. A 117 610
3. Feshbach H and Villars F 1958 Rev. Mod. Phys. 30 24.
4. Equation (2.15) in their paper is the two-component spin-0 equation that we denote as 'the Feshbach-Villars equation', or 'the FV0 equation' for convenience. In discussing this equation, authors generally refer to the paper of Feshbach and Villars, despite the fact that its content is largely based upon earlier material, in particular Taketani M and Sakata S 1940 Proc. Math. Phys. Soc. Japan 22 757
5. Heitler W 1943 Proc. Roy. Irish. Acad. 49 1.
6. Taketani and Sakata were the first to write Kemmer's (Kemmer N 1939 Proc. R. Soc. A 173 91) ten-component first-order equation for spin-1 particles as a six-component equation in Hamiltonian form. The two-component spin-0 equation (for free particles) is easily deduced from the six-component equation, as shown by Heitler. Heitler also gives an extensive discussion of the spin-0 equation, much of which is used by Feshbach and Villars in their paper. Feshbach and Villars, however, were the first to write the equation with a minimal coupling, and also to derive the equation directly from the Klein-Gordon equation by linearizing the time derivative. This method of derivation is referred to as 'the Feshbach-Villars linearization procedure'.
7. Petroni N C, Gueret P, Vigier J P and Kypnanidis A 1986 Phys. Rev. D 33 1674 (equation (1.2)) and references therein.
8. Feynman R P and Gell-Mann M 1958 Phys. Rev. 109 193 consider especially one of the decoupled parts of the equation in the Weyl representation of the gamma matrices, equation (6) in their paper. The full equation is given by equation (3) in their paper.
9. Lifshitz E M, Berestetskiǐ V B and Pitaevskiǐ L P 1974 Relativistic Quantum Theory (Oxford: Pergamon) ch 3
10. T
11. Petroni N C, Gueret P, Vigier J P and Kyprianidis A 1985 Phys. Rev. D 31 3157
12. Feynman R P 1961 Quantum Electrodynamics equation (9.4)
13. Actually an extension of H should eventually be considered. See for example Capri A Z 1985 Non-relativistic Quantum Mechanics (Menlo Park: Benjamin-Cummings)
14. Pease M C 1965 Matrix Algebra (New York: Academic)
15. Greiner W 1989 Quantum Mechanics: An Introduction (Berlin: Springer)
16. Bjorken J D and Drell S D 1964 Relativistic Quantum Mechanics (New York: McGraw-Hill)
17. In fact both of the KG0 and KG1/2 equations are partial differential equations of the second order in each of the four variables t and x. The Feshbach-Villars linearization procedure is concerned with the mathematical reduction of just the time derivative to first order, as the Hamiltonian form in quantum mechanics only requires this. Alternatives (especially Petroni N C, Gueret P and Vigier J P 1988 Found. Phys. 18 1057) will be discussed in a future paper.
18. Greiner W 1990 Relativistic Quantum Mechanics (Berlin: Springer)
19. Bethe H A and Salpeter E E 1977 Quantum Mechanics of One and Two Electron Atoms (New York: Plenum)
20. Auvil P R and Brown L M 1975 Am. J. Phys. 46 679
21. Davis L 1939 Phys. Rev. 56 186
22. m. is given according to [5], p 108, where R(r) is an arbitrary function of r. Then the linear combinations and derivatives of confluent hyergeometric functions can be simplified using results given in Slater, pp 15 and 19.